Fillmore--Springer--Cnops Construction Implemented in GiNaC

Details Fillmore--Springer--Cnops Construction Implemented in GiNaC Fillmore--Springer--Cnops Construction Implemented in GiNaC

2005-12-17

arxiv.org/abs/cs/0512073v10

Adv. Appl. Clifford Algebr. v.17 (2007), no.1, 59-70

Computer Science

Mathematical Software

LaTeX, 79 p; 9 PS graphics in one figure, the full source files and ISO image of Live DVD are included, see last section of th

Scientific paper

10.1007/s00006-006-0017-4

This paper presents an implementation of the Fillmore--Springer--Cnops construction (FSCc) along with illustrations of its usage. FSCc linearises the linear-fraction action of the Moebius group in R^n. This has clear advantages in several theoretical and applied fields including engineering. Our implementation is based on the Clifford algebra capacities of the GiNaC computer algebra system (http://www.ginac.de/), which were described in cs.MS/0410044. The core of this realisation of FSCc is done for an arbitrary dimension of R^n with a metric given by an arbitrary bilinear form. We also present a subclass for two dimensional cycles (i.e. circles, parabolas and hyperbolas), which add some 2D specific routines including a visualisation to PostScript files through the MetaPost (http://www.tug.org/metapost.html) or Asymptote (http://asymptote.sourceforge.net/) packages. This software is the backbone of many results published in math.CV/0512416 and we use its applications their for demonstration. The library can be ported (with various level of required changes) to other CAS with Clifford algebras capabilities similar to GiNaC. There is an ISO image of a Live Debian DVD attached to this paper through the Data Conservancy data repository.

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